What is 255 in Binary? - How-to & Steps

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  • 0:04 255 in Binary Numbers
  • 1:55 Alternate Conversion Methods
  • 3:53 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Binary math uses a base 2 number system, and is the foundation of the on-off way of thinking for computers. In this lesson, we'll discover how to reach the decimal value 255 using binary numbers.

255 in Binary Numbers

Briefly stated, you can get to 255 very quickly using binary (base 2) numbers, because 255 is 1 less than 256, which is 2 to the 8th power (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2). Any power of 2 is expressed in binary as a 1 with a number of 0's following, equal to that power. For instance, 16 is 2^4 (or 1 with four zeroes in binary).

Power of 2 Decimal Value Binary Value
0 1 1 (no zeroes)
1 2 10 (one zero)
2 4 100 (two zeroes)
3 8 1000 (three zeroes)
4 16 10000 (four zeroes)
5 32 100000 (five zeroes)
6 64 1000000 (six zeroes)
7 128 10000000 (seven zeroes)
8 256 100000000 (eight zeroes)

See the pattern? In binary, 2's are like 10's are in the decimal system. In the decimal system, 9 comes before 10. 99 comes before 100. 999 comes before 1000. In binary, it's all 1's and 0's. So, the step before 256 is all 1's. Therefore, 255 in binary is 11111111.

The step before any power of 2 is a string of 1's. Just like 9 comes before 10 in decimal, 1 comes before 10 in binary. There are as many 1's as the number of the power that is the next step.

Power of 2 Decimal Value Decimal Value Minus 1 Binary Value
0 1 0 0 (no 1's)
1 2 1 1 (one 1)
2 4 3 11 (two 1's)
3 8 7 111 (three 1's)
4 16 15 1111 (four 1's)
5 32 31 11111 (five 1's)
6 64 63 111111 (six 1's)
7 128 127 1111111 (seven 1's)
8 256 255 11111111 (eight 1's)

256 would be expressed in binary by 100000000, a 1 with eight 0's, since it's 2 to the eighth power, so binary 255 would be the step before that, which would be 11111111 (eight 1's in a row). Any number that is 1 less than a power of 2 will be merely a string of 1's equal to that number's power.

So again, we see that 255 in binary is written as 11111111.

Alternate Conversion Methods

The general steps for converting a decimal into a binary number are simple:

  1. Determine if the number is odd or even. If the number is odd. If the number is odd, write a 1 for the next lowest digit and subtract 1 from the number.
  2. If the number is even, write a 0 for the next lowest digit and don't subtract anything.
  3. Divide by 2.
  4. Continue these steps until you've reached 0.

Our 255 would come out like this:

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